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Lena loves limits because they help her visualize the graphs of complicated looking functions. For example, by evaluating the limit as as , she can determine if a rational function such as will have a horizontal asymptote or not.

Evaluate each limit below and explain to Lena how she can determine without graphing. (Be careful! The expressions below are all slightly different.)

  1. Compare the highest power in the numerator and the denominator small exponent on top large exponent on the bottom.

  1. As , only the highest power of the numerator and denominator is powerful enough to affect the end behavior of a function.

  1. Limit Does Not Exist but